(6+z)(2z+9)=0

Solution for (6+z)(2z+9)=0 equation:

(6+z)(2z+9)=0

We add all the numbers together, and all the variables

(z+6)(2z+9)=0

We multiply parentheses ..

(+2z^2+9z+12z+54)=0

We get rid of parentheses

2z^2+9z+12z+54=0

We add all the numbers together, and all the variables

2z^2+21z+54=0

a = 2; b = 21; c = +54;
Δ = b2-4ac
Δ = 212-4·2·54
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3}{2*2}=\frac{-24}{4}
=-6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3}{2*2}=\frac{-18}{4}
=-4+1/2
$